#include #define whlie while #define pb push_back #define eb emplace_back #define fi first #define se second #define rep(i,N) for(int i = 0; i < (N); i++) #define repr(i,N) for(int i = (N) - 1; i >= 0; i--) #define rep1(i,N) for(int i = 1; i <= (N) ; i++) #define repr1(i,N) for(int i = (N) ; i > 0 ; i--) #define each(x,v) for(auto& x : v) #define all(v) (v).begin(),(v).end() #define sz(v) ((int)(v).size()) #define vrep(v,it) for(auto it = v.begin(); it != v.end(); it++) #define vrepr(v,it) for(auto it = v.rbegin(); it != v.rend(); it++) #define ini(...) int __VA_ARGS__; in(__VA_ARGS__) #define inl(...) ll __VA_ARGS__; in(__VA_ARGS__) #define ins(...) string __VA_ARGS__; in(__VA_ARGS__) using namespace std; void solve(); using ll = long long; using vl = vector; using vi = vector; using vvi = vector< vector >; constexpr int inf = 1001001001; constexpr ll infLL = (1LL << 61) - 1; struct IoSetupNya {IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7);} } iosetupnya; template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template ostream& operator <<(ostream& os, const pair &p) { os << p.first << " " << p.second; return os; } template istream& operator >>(istream& is, pair &p) { is >> p.first >> p.second; return is; } template ostream& operator <<(ostream& os, const vector &v) { int s = (int)v.size(); rep(i,s) os << (i ? " " : "") << v[i]; return os; } template istream& operator >>(istream& is, vector &v) { for(auto &x : v) is >> x; return is; } void in(){} template void in(T &t,U &...u){ cin >> t; in(u...);} void out(){cout << "\n";} template void out(const T &t,const U &...u){ cout << t; if(sizeof...(u)) cout << " "; out(u...);} templatevoid die(T x){out(x); exit(0);} #ifdef NyaanDebug #include "NyaanDebug.h" #define trc(...) do { cerr << #__VA_ARGS__ << " = "; dbg_out(__VA_ARGS__);} while(0) #define trca(v,N) do { cerr << #v << " = "; array_out(v , N);cout << endl;} while(0) #else #define trc(...) #define trca(...) int main(){solve();} #endif using P = pair; using vp = vector

; constexpr int MOD = /** 1000000007; //*/ 998244353; //////////////// template struct DynamicLiChaoTree{ struct Line{ T slope , intercept; Line() : slope(0),intercept(INF){} Line(T slope,T intercept) : slope(slope),intercept(intercept){} inline T get(T x) const{ return slope * x + intercept; } inline bool over(const Line& other , const T &x) const{ return get(x) < other.get(x); } }; // remind セグ木は1-indexedの実装 T xmin, xmax, _size; unordered_map seg; // [l , r]におけるLi Chao Tree DynamicLiChaoTree(T xmin, T xmax) : xmin(xmin), xmax(xmax){ _size = 1; while(_size < xmax - xmin + 1) _size <<= 1; } // 内部用の関数 void update(T a,T b,T left,T right,T seg_idx){ Line line(a , b); while(1){ int mid = (left + right) >> 1; bool l_over = line.over(seg[seg_idx], min(xmax , left + xmin) ); bool r_over = line.over(seg[seg_idx], min(xmax , right-1+ xmin) ); if(l_over == r_over){ if(l_over) swap(seg[seg_idx] , line); return; } bool m_over = line.over(seg[seg_idx], min(xmax , mid + xmin) ); if(m_over) swap(seg[seg_idx], line); if(l_over != m_over) seg_idx = (seg_idx << 1) , right = mid; else seg_idx = (seg_idx<<1) | 1 , left = mid; } } // 内部用の関数 void update(T a, T b, T seg_idx){ T left , right; T upper_bit = 63 - __builtin_clzll(seg_idx); left = (_size >> upper_bit) * (seg_idx - (1 << upper_bit) ); right = left + (_size >> upper_bit); update(a , b , left , right , seg_idx); } /* void update(T a,T b,T left,T right){ T lower_bit = (left | right) & (- (left | right) ); T seg_idx = ( _size + left ) / lower_bit; update(a , b , left , right , seg_idx); } */ // y = ax + bなる直線を追加 void update(T a, T b){ update(a , b , 0 , _size , 1); } // 閉区間x in [left , right]に線分y = ax + bを追加するクエリ void update_line_segment(T a,T b,T left,T right){ left -= xmin - _size, right -= xmin - _size - 1; for( ; left < right; left >>= 1 , right >>= 1){ if(left & 1) update(a , b , left++); if(right& 1) update(a , b , --right); } } // xにおける最小値クエリ T query(T x) { T left = 0 , right = _size , seg_idx = 1 , idx = x - xmin , ret = INF; while(1){ T cur = seg[seg_idx].get(x); //if(cur == INF) break; ret = min(ret , cur); if(left + 1 >= right) break; int mid = (left + right) >> 1; if(idx < mid) seg_idx = (seg_idx << 1) , right = mid; else seg_idx = (seg_idx << 1) | 1 , left = mid; } return ret; } void merge(DynamicLiChaoTree &other){ if(seg.size() < other.seg.size()) seg.swap(other.seg); for(auto &x : other.seg){ if(x.second.intercept == INF) continue; update(x.second.slope , x.second.intercept , x.first); } } }; void solve(){ ini(N); vl a(N) , x(N) , y(N); in(a , x , y); vl dp(N , 0); DynamicLiChaoTree lichao(0 , 100000); lichao.update_line_segment(1 , y[0] - x[0] , x[0] , 100000); lichao.update_line_segment(-1, y[0] + x[0] , 0 , x[0]); each(x , lichao.seg) trc(x.first, x.second.slope , x.second.intercept); rep(i,N){ if(i){ lichao.update_line_segment(1 , dp[i-1] + y[i] - x[i] , x[i] , 100000); lichao.update_line_segment(-1, dp[i-1] + y[i] + x[i] , 0 , x[i]); } dp[i] = lichao.query(a[i]); } trc(dp); out(dp[N - 1]); }